3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1 – cos t) te [0, 7]. (a) Show that x' (t) = sin 2t – sin t, y'(t) = cost – cos 2t. 1
3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1 – cos t) te [0, 7]. (a) Show that x' (t) = sin 2t – sin t, y'(t) = cost – cos 2t. 1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please answer all the parts
![3. Consider the parameteric equations for a curve C given by
x(t) = cos t(1 – cos t), y(t) = sin t(1 – cos t) te [0, ].
(a) Show that
x' (t)
= sin 2t – sin t, y'(t)
= Cost – cos 2t.
1
(b) Compute [a' (t)]² + [y/ (t)]².
(Hint: your answer will involve sin 2t sin t and cos 2t cos t, you can then simplify
further using a sum-angle identity).
(c) Use earilier parts to compute the legth of the curve C parameterized by x(t)
and y(t) for t E [0, 1]. (Hint: you might have use for one of the half-angle trig
identities.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56cb530e-79f5-4435-9333-7389d1b24ae9%2F2069593c-1045-4986-9db7-198b2b39664b%2Frbkgwu9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the parameteric equations for a curve C given by
x(t) = cos t(1 – cos t), y(t) = sin t(1 – cos t) te [0, ].
(a) Show that
x' (t)
= sin 2t – sin t, y'(t)
= Cost – cos 2t.
1
(b) Compute [a' (t)]² + [y/ (t)]².
(Hint: your answer will involve sin 2t sin t and cos 2t cos t, you can then simplify
further using a sum-angle identity).
(c) Use earilier parts to compute the legth of the curve C parameterized by x(t)
and y(t) for t E [0, 1]. (Hint: you might have use for one of the half-angle trig
identities.)
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